Running head: PROBABILISTIC CLUSTERING THEORY OF VSTM 1 A Probabilistic Clustering Theory of the Organization of Visual Short-Term Memory

Experimental evidence suggests that the content of a memory for even a simple display encoded in visual short-term memory (VSTM) can be very complex. VSTM uses organizational processes that make the representation of an item dependent on the feature values of all displayed items as well as on these items’ representations. Here, we develop a Probabilistic Clustering Theory (PCT) for modeling the organization of VSTM for simple displays. PCT states that VSTM represents a set of items in terms of a probability distribution over all possible clusterings or partitions of those items. Because PCT considers multiple possible partitions, it can represent an item at multiple granularities or scales simultaneously. Moreover, using standard probabilistic inference, it automatically determines the appropriate partitions for the particular set of items at hand, and the probabilities or weights that should be allocated to each partition. A consequence of these properties is that PCT accounts for experimental data that have previously motivated hierarchical models of VSTM, thereby providing an appealing alternative to hierarchical models with pre-specified, fixed structures. We explore both an exact implementation of PCT based on Dirichlet process mixture models, and approximate implementations based on Bayesian finite mixture models. We show that a previously proposed two-level hierarchical model can be seen as a special case of PCT with a single cluster. We show how a wide range of previously reported results on the organization of VSTM can be understood in terms of PCT. In particular, we find that, consistent with empirical evidence, PCT predicts biases in estimates of the feature values of individual items, and also predicts a novel form of dependence between estimates of the feature values of different items. We qualitatively confirm this last prediction in three novel experiments designed to directly measure biases and dependencies in subjects’ estimates. PROBABILISTIC CLUSTERING THEORY OF VSTM 3 A Probabilistic Clustering Theory of the Organization of Visual Short-Term Memory